SCNC1111 Scientific Method and Reasoning

Part I: The Nature and Methodology of Science

Lecture 2 What Are Good Theories?

and Two Simplifications of the Idealized Scientific Method

2014 09 12 Dr. William M.Y. Cheung

Reminders! Tutorial sessions on Tuesday (1B, 1C and 1D) have no

tutorial this week. Next week students in these sessions will go through the

same materials covered in other tutorial sessions this week. (You wont miss anything!)

In the tutorial next week, we will initiate our work on the Group Project. Again students belonging to the Tuesday sessions will have

to wait until 23 September, 2014. Stay tuned!

Assignment 1 due 16:55, 25 September, 2014 Check our main Moodle course website!

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Summary of the Idealized Scientific Method Observation

Hypothesis

Prediction

Experimental Test

Confirmation or Falsification

This rough sketch of scientific method should not be taken too literally!

(Generalization via

induction)

(Deduction)

(Dis)Proving Theories So what has Feynman told us this time? 1. Compare Predictions from your Theory with

Observations as much as possible 2. Theories can only be falsified

when its predictions disagree with observations 3. We are never sure if a theory is 100% correct

maybe we just have not seen its discrepancies yet

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Beyond the Scientific Method Scientific investigation requires guidance beyond the

Scientific Method How should we compare theories devised to explain the

same phenomena? What qualifies as a good theory?

A good theory cannot be ambiguous!

Predictions from our theory should be as concrete and precise as possible.

Mathematics help us to be concrete and precise!

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A Reflection about Economics

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vs

economist

"utility = the amount of "satisfaction" I get via

consumption of the goods under concern

utility = 70 units utility = 90 units

Utility What is wrong with this?

Can you predict how many customers will prefer noodles over rice this afternoon at the CYM canteen?

Such utility function is different for different person. i.e. we all have different preferences

Even for the same person, such utility function changes over time. i.e. I may prefer different cuisines on different days

What can we predict?

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Another Criterion http://www.ted.com/talks/david_deutsch_a_new_w

ay_to_explain_explanation.html (9:14 16:39)

Being testable/falsifiable is not enough! Good explanations: hard to vary

but still explain the phenomena every detail of the explanations is needed for the

explanations Beware of explanationless theories

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Unknown Parameters Theories built on assumptions, e.g.

masses attract each other via gravity electrons and the nucleus attract because they carry

opposite charges Theories contain unknown parameters that the

theories themselves cannot explain, e.g. Universal Gravitational Constant G (Physics) Electric charge of an electron (Chemistry)

What should we do? My theory cannot tell me the values of these parameters How can I make quantitative predictions?

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Predicting with Parameters Measure these parameters via experiments Use these experimentally obtained values to make

MORE quantitative predictions Compare these predictions with OTHER experiments

to confirm/falsify your theories

Have as few parameters (assumptions) as possible, and make as many predictions as possible!

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YipKam Kai Wilson

YipKam Kai Wilsonunknown parameters

Polynomial Fitting

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Y

X

= +

Polynomial Fitting

12

Y

X

= + +

Polynomial Fitting

13

Y

X

= + +

+

Polynomial Fitting Whats wrong with this?

We are using 4 data points to determine 4 unknown parameters We are not predicting anything! We can always pass through n data points using a

polynomial with n coefficients! 14

= + + +

unknown parameters to be determined from our (experimental) data points

A Fallacy Imagine a new experimental result does not agree with an

existing theory Falsification! This theory need to be modified, if not thrown away

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We can add a new term to the theory to explain the new experimental result!

This new term carries an unknown parameter. How

can we determine its value?

The value of this new parameter

must be one that reproduces the new experimental result.

A Fallacy Imagine a new experimental result does not agree with an

existing theory Falsification! This theory need to be modified, if not thrown away

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You are using the new experimental result as an

input to your new theory. You are not explaining it! Where is the

prediction of your new theory?

The value of this new parameter

must be one that reproduces the new experimental result.

Occams Razor What should we do if

Two theories both succeed in explaining the same phenomena

No available experiments can falsify one of them

Which one should we prefer?

Occams Razor http://www.youtube.com/watc

h?v=oAp3jT8n6Qs

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Occams Razor All things being equal, the simplest explanation

tends to be the right one. E.g. I used my staff card this morning, but now I

cannot find it in my office. Explanation 1: I misplaced my staff card somewhere else. Explanation 2: Someone (one of you, a fairy, etc.) broke

into my office, stole my staff card but leaving no trace. Which one would you prefer? Recall

Feynman discussed flying saucers in the video Have as few assumptions as possible!

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Caution! Occams Razor is only a philosophical guiding

principle. Used when currently available evidences do not

favour one theory over the other No reason why simpler theories always have to be

correct Later experiments may favour the more complicated

theory and falsify the simpler one.

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Some Criteria on Good Theory A good theory cannot be ambiguous!

Predictions from our theory should be as concrete and precise as possible.

Mathematics help us to be concrete and precise! Should not be easily varied Be able to make many predictions with as few

parameters as possible Occams Razor

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A Quote

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The Nature of Scientific Practice

We are now going to discuss two key simplifications made by our scientific method: The theoretical basis of observation. The complexity of hypothesis testing.

These examples teach us that there is no clear separation or straightforward relationship between theory, observation, and experiment.

Theory Experiment

& Observation

http://mirror-uk-rb1.gallery.hd.org/ http://organizationalpsychologies.com/

Effective Observation needs Theory

Adam Hart-Davis

Recall the requirement that observations should be made under a wide variety of circumstances before making a generalization:

What factors are significant in determining the boiling point of water?

A. Air pressure

B. Purity of the water

C. Method of heating

D. Material of the container

E. Geographical location

Effective Observation needs Theory

Adam Hart-Davis

Recall the requirement that observations should be made under a wide variety of circumstances before making a generalization:

What factors are significant in determining the boiling point of water?

A. Air pressure

B. Purity of the water

C. Method of heating

D. Material of the container

E. Geographical location

How do you know what factors are

significant?

What if you are the first scientist to

study this?

Example: Hertz and the Detection of Radio Waves

http://okinawa.nict.go.jp

Example: Hertz and the Detection of Radio Waves

If Hertz were totally unguided by theory in the observations that he made, he would have had to record: the appearance of sparks at the critical locations in

his electrical circuit dimensions of his circuit colour of the meters dimensions of the laboratory the state of the weather size of his shoes, etc. Hertz never, in fact, arrived at the correct speed of radio waves because their reflection from the walls of his laboratory interfered with his results. The dimensions of Hertzs laboratory were in fact highly relevant!

27 http://es.wikipedia.org

Heinrich Hertz (1857-94)

Effective Observation needs Theory

Significant factors can only be distinguished from irrelevant ones by bringing in our theoretical knowledge of the situation.

Unless we can eliminate some irrelevant factors, well never be able to generalize.

Since we dont know in advance what factors are relevant, we need some theory to guide us.

Observations are Always Made Using Theoretical Language

Compare the following observation statements: A. The electron beam was repelled by the North Pole of

the magnet. B. The gas in the cooker wouldnt light. C. The heart is pumping blood around the body.

As science progresses, new theoretical terms are invented and become part of our observational language.

The theoretical basis of observation!

The Complexity of Hypothesis Testing FAULT CAUSE Strong vibrations during spin

Washing machine not perfectly level Transport bracket not removed Washing load not evenly distributed

Does not function on any programme

Mains plug not plugged in Mains switch not on No power Electric circuit fuse failure Load door open

REMEDY Adjust special feet Remove transport bracket Distribute washing evenly Insert plug Turn on mains switch Check Check Close load door

When something is not working properly (i.e. a mismatch between theory and experiment), there are many possible explanations.

A hypothesis may not (and need not) be completely discarded right away.

Example: Testing an Astronomical Theory To derive a prediction of the position of a planet observed through a telescope, we will need:

zA prediction derived from the theory under test.

zPrevious positions of the planet and the Sun and possibly other planets (initial conditions).

zCorrections to the path of the light through the Earths atmosphere (optical theory).

If the planet is not seen at the predicted position, any one of these factors may be at fault!

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Example: Testing an Astronomical Theory

This is why theories are not abandoned immediately following

an unfavourable experimental outcome!

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Before the invention of the telescope, it was universally

accepted that the size of Venus did not vary throughout the year.

But it assumed that the size of small light sources can be estimated accurately with the naked eye.

Example: Observations of the Size of Venus

Source: wikipedia

This was in direct contradiction with the Copernican (sun-centered)

theory of the universe!

Before the invention of the telescope, it was universally

accepted that the size of Venus did not vary throughout the year.

But it assumed that the size of small light sources can be estimated accurately with the naked eye.

Example: Observations of the Size of Venus

Source: wikipedia

This was in direct contradiction with the Copernican (sun-centered)

theory of the universe!

Observation statements are never absolutely certain!

Example: Testing an Astronomical Theory and Discovery!

zNineteenth-century observations of the planet Uranus diverged considerably from predictions based on Newtons theory.

zThis was because they failed to take into account the existence of a new planet, later named Neptune.

An apparent falsification was turned into a triumphant confirmation!

Source: NASA

Summary There is no clear separation or straightforward relationship between theory, observation, and experiment: The theoretical basis of observation:

We make theoretical assumptions about relevant factors. Theory is built into even our most basic observation

statements.

The complexity of hypothesis testing: We need additional data, assumptions, and auxiliary

theories to test a hypothesis. Observation statements and experiments are never totally

beyond doubt.